Optics: measuring and testing – By polarized light examination – With light attenuation
Reexamination Certificate
1998-11-23
2001-07-03
Font, Frank G. (Department: 2877)
Optics: measuring and testing
By polarized light examination
With light attenuation
Reexamination Certificate
active
06256098
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates methods for determining and designing optical elements such as lenses and mirrors, in general, and to a method for determining and designing the topography of optical elements, in particular.
BACKGROUND OF THE INVENTION
Methods for determining and designing optical elements, such as lenses and mirrors, are known in the art. These methods attempt to provide accurate surfaces for uni-focal optical elements and near accurate surfaces for multi-focal optical elements. Multi-focal lenses and mirrors provide a plurality of focal points, each for a different area in the optical element.
When designing an optical element, the designer determines a list of requirements which restrict the final result. Such requirements can include a general geometry of the requested surface, a collection of optical paths which have to be implemented in the requested surface and the like. Such optical paths can be determined in theory or as measurements of the paths of light rays, which include a plurality of rays, through the optical element.
According to one method, which is known in the art, an optical surface is determined according to a preliminary given surface, which is characterized by a finite number of parameters. The method calculates an optimal choice of the parameters, thereby determining the desired optical surface. The representation of the calculated optical surface can be given by polynomials or other known special functions.
It will be appreciated by those skilled in the art that such optical surfaces are limited in that the optimization is obtained according to a limited and finite number of parameters, while the number of restrictions can be significantly larger.
G. H. Guilino, “Design Philosophy For Progressive Addition Lenses”, Applied Optics, vol. 32, pp. 111-117, 1993, provides a thorough survey of the methods for design principles of multi-focal lenses.
U.S. Pat. No. 4,315,673, to Guilino et al. is directed to a progressive power ophthalmic lens. Guilino describes a specific geometry, which utilizes specific functions to achieve an optical surface with varying power.
U.S. Pat. No. 4,606,622 to Fueter et al. is directed to a multi-focal spectacle lens with a dioptric power varying progressively between different zones of vision. Fueter describes a method for determining a surface according to a plurality of points. The method defines a twice continuously differentiable surface through these points. The surface is selected so as to achieve a varying optical surface power.
SUMMARY OF THE INVENTION
It is an object of the invention to provide a novel method for determining surfaces of optical elements, which overcome the disadvantages of the prior art.
In accordance with the present invention there is thus provided a method for determining an optical surface, including the steps of: receiving data relating to a plurality of rays and to a plurality of affected rays, wherein each of the rays is associated with a respective affected ray, determining a set of integration equations from the data, and determining the optical surface from the set of equations.
According to one aspect of the invention, the affected rays are refracted by the optical surface while according to another aspect of the invention the affected rays are reflected by the optical surface.
The step of determining the optical surface can include the sub-steps of: detecting if the set of integration equations is solvable, integrating the set of integration equations when the set of integration equations is solvable, thereby determining the optical surface, determining a cost function and auxiliary conditions for the set of integration equations, when the set of integration equations is not solvable, and optimizing the cost function, subject to the auxiliary conditions, thereby determining the optical surface.
The data which is used by the method can be received from a measurement system or from a user.
According to a further aspect of the invention, the method can further include the step of determining a reference plane from the ray related data, when the ray related data is provided with respect to a non planar surface.
For example, the integration equations can include:
f
x
=
u
1
+
f
[
u
1
(
cos
α
cot
β
)
x
+
u
2
(
sin
α
cot
β
)
x
]
1
-
cot
β
(
u
1
cos
α
+
u
2
sin
α
)
=
F
1
,
f
y
=
u
2
+
f
[
u
1
(
cos
α
cot
β
)
y
+
u
2
(
sin
α
cot
β
)
y
]
1
-
cot
β
(
u
1
cos
α
+
u
2
sin
α
)
=
F
2
.
wherein
u
1
=
n
2
a
-
n
1
cos
α
cos
β
n
1
sin
β
-
n
2
c
,
u
2
=
n
2
b
-
n
1
sin
α
cos
β
n
1
sin
β
-
n
2
c
,
x and y denote the geometrical location of each of the rays on the reference plane,
n
1
denotes the optical index with respect to the rays,
n
2
denotes the optical index with respect to the affected rays,
f denotes the height of the optical surface above the reference plane,
(cos &agr; cos &bgr;, sin &agr; cos &bgr;, sin &bgr;) denotes the direction vector of each of the rays, and
(a,b,c) denotes the direction vector of each of the affected rays.
Alternatively, the integration equations can include:
f
x
=
u
1
+
f
[
u
1
(
cos
α
cot
β
)
x
+
u
2
(
sin
α
cot
β
)
x
]
1
-
cot
β
(
u
1
cos
α
+
u
2
sin
α
)
=
F
1
,
f
y
=
u
2
+
f
[
u
1
(
cos
α
cot
β
)
y
+
u
2
(
sin
α
cot
β
)
y
]
1
-
cot
β
(
u
1
cos
α
+
u
2
sin
α
)
=
F
2
.
wherein
u
1
=
n
2
Δ
x
-
n
1
D
cos
α
cos
β
n
1
D
sin
β
-
n
2
Δ
z
,
u
2
=
n
2
Δ
y
-
n
1
D
sin
α
sin
β
n
1
D
sin
β
-
n
2
Δ
z
,
&Dgr;x=&zgr;−
(
x+f
cos &agr; cot &bgr;),
&Dgr;y=&eegr;−
(
y+f
sin &agr; cot &bgr;),
&Dgr;z=h−f
and
D={square root over (&Dgr;x
2
+&Dgr;y
2
+&Dgr;z
2
+L )}.
(&zgr;(x,y),&eegr;(x,y),h(x,y)) denotes the geometrical location of each of the affected rays,
x and y denote the geometrical location of each of the rays on a reference plane,
n
1
denotes the optical index with respect to the rays,
f denotes the height of the optical surface above the reference plane,
n
2
denotes the optical index with respect to the affected rays, and
(cos &agr; cos &bgr;, sin &agr; cos &bgr;, sin &bgr;) denotes the direction vector of each of the rays.
The step of determining the optical surface can include the steps of: detecting if the set of integration equations is solvable, integrating the set of integration equations when the set of integration equations is solvable, thereby determining the optical surface, determining a cost function and auxiliary conditions for the set of integration equations, when the set of integration equations is not solvable, optimizing the cost function, subject to the auxiliary conditions, thereby determining the optical surface, where
Rubinstein Jacob
Wolansky Gershon Moshe
Eitan Pearl Latzer & Cohen-Zedek
Font Frank G.
Inray Ltd.
Nguyen Tu T.
LandOfFree
Method for determining and designing optical elements does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Method for determining and designing optical elements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method for determining and designing optical elements will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2564098